Stream Stage Fluctuations Research Articles

Aquifer Response to Stream-Stage Fluctuations: Field Tests and Analytical Solution for a Case Study of the Yangtze River in Wuhan, China

In this paper, field hydrological monitoring tests and an analytical solution for the aquifer response (i.e., the groundwater head) to stream-stage fluctuations are presented through a case study of the Yangtze River in Wuhan, China. A sinusoidal equation for the stream water level over time is proposed and is verified by the monitoring results. Based on the classical 1-D solution of ground water flow equations, a new flow model was proposed to analyze the confined aquifer response to stream-stage fluctuations. The groundwater head of the confined aquifer can then be calculated by embedding the proposed sinusoidal equation of the stream-stage fluctuation into the new flow model. Field monitoring data of the three hydrological years from 2017 to 2019 were compiled to evaluate the proposed model. The results show that the predicted groundwater head of the confined aquifer matches well with the monitoring data. The prediction error of the proposed model (about 8%) is much lower than that of the previous model (about 26%). This paper presents an improved analytical model with a satisfying capability to predict the response of the groundwater head of the confined aquifer to stream-stage fluctuation. This model can be applied into groundwater flow models (such as MODFLOW, FEFLOW, etc.). The results of this study provide a valuable hydrological resource for underground practical engineering in the riverside area, especially in the first terrace of the Yangtze River, and for the dewatering design of a foundation pit in a riverside area.

Hyporheic exchange mechanism driven by flood wave

AbstractTo study the hyporheic exchange driven by a single peak flood‐induced water level fluctuation (i.e., flood wave), a method combining numerical simulation with theoretical derivation was proposed based on the Inbuk Stream, Korea, where flooding occurs frequently. The hyporheic exchanges induced by different flood waves were investigated by varying amplitude (A), duration (T), wave type parameter (r), and rising duration (tp), which were adopted from the real‐time stream stage fluctuations. Additionally, the idea of constant upstream flood volume (CUFV) condition for flood waves was put forward, and the effects of “Botan” (T/A) and peak number (N) on hyporheic exchange were studied. The results showed that the hyporheic exchange flux (q) was controlled by the water level h (sine‐type) and its change rate v (cosine‐type), and was proportional to the polynomial of them q ∝ (ω∙h + v), where ω is the angular frequency of the flood wave. Based on this mechanism, the influence principles on hyporheic exchanges of the typical flood wave parameters (A, T, r and tp) as well as T/A and N under CUFV condition were clarified. The main characteristic variables of hyporheic exchange, which were maximum aquifer storage and residence time, were positively correlated. They also had positive relations to the integral of the flood wave over time, which increased when the wave became higher, wider, rounder and less skewed. However, when CUFV condition was imposed, the residence time was positively correlated with T/A, whereas the maximum aquifer storage was negatively correlated with T/A. With the increase in N, water exchanged more frequently and some water returned to the stream early, leading to the slight decrease in maximum aquifer storage and residence time. These findings enriched the theory of hyporheic exchange driven by surface water fluctuation and be of great significance to enhance pollutant degradation in the hyporheic zone downstream of reservoirs.

Solute dynamics across the stream‐to‐riparian continuum under different flood waves

AbstractTo enhance the understanding of solute dynamics within the stream‐to‐riparian continuum during flood event‐driven water fluctuation (i.e., flood wave), a variable saturated groundwater flow and solute transport model were developed and calibrated against in situ measurements of the Inbuk stream, Korea, where seasonal flooding prevails. The solute dynamics were further investigated for flood waves (varying by amplitude [A], duration [T], roundness [r], and skewness [tp]) that were parameterised by real‐time stream stage fluctuations. We found that the solute transferred faster and farther in the riparian zone, especially within the phreatic zone, above which in the variable saturated zone the concentration required a significantly longer time, particularly at higher altitudes, to return to the initial state. By comparison, solute transferred shallowly in the streambed where the solute plume exhibited an exponential growth trend from the centre to the bank. The dynamic changes of solute flux and mass along the stream–aquifer interface and stream concentration were linked to the shape of flood wave. As the flood wave became higher (A↗), wider (T↗), rounder (r↘), and less skewed (tp↗), the maximum solute storage in aquifer increased. Maximum stream concentration (Cstrˍmax) not only presented a positive linear relationship with A or tp but also showed a negative logarithmic trend with increasing T or r. The sensitivity of Cstr_max to A was approximately two times that of tp, and between these values, the r was slightly more sensitive than T. Cstrˍmax linearly increased as hydraulic conductivity increased and logarithmically increased as longitudinal dispersivity increased. The former relationship was more sensitive than the latter.

Modeling the Impact of Stream Discharge Events on Riparian Solute Dynamics.

The biogeochemical composition of stream water and the surrounding riparian water is mainly defined by the exchange of water and solutes between the stream and the riparian zone. Short-term fluctuations in near stream hydraulic head gradients (e.g., during stream flow events) can significantly influence the extent and rate of exchange processes. In this study, we simulate exchanges between streams and their riparian zone driven by stream stage fluctuations during single stream discharge events of varying peak height and duration. Simulated results show that strong stream flow events can trigger solute mobilization in riparian soils and subsequent export to the stream. The timing and amount of solute export is linked to the shape of the discharge event. Higher peaks and increased durations significantly enhance solute export, however, peak height is found to be the dominant control for overall mass export. Mobilized solutes are transported to the stream in two stages (1) by return flow of stream water that was stored in the riparian zone during the event and (2) by vertical movement to the groundwater under gravity drainage from the unsaturated parts of the riparian zone, which lasts for significantly longer time (> 400 days) resulting in long tailing of bank outflows and solute mass outfluxes. We conclude that strong stream discharge events can mobilize and transport solutes from near stream riparian soils into the stream. The impact of short-term stream discharge variations on solute exchange may last for long times after the flow event.

Groundwater response to serial stream stage fluctuations in shallow unconfined alluvial aquifers along a regulated stream (West Virginia, USA)

Groundwater response to stream stage fluctuations was studied in two unconfined alluvial aquifers using a year-long time series of stream stages from two pools along a regulated stream in West Virginia, USA. The purpose was to analyze spatial and temporal variations in groundwater/surface-water interaction and to estimate induced infiltration rate and cumulative bank storage during an annual cycle of stream stage fluctuation. A convolution-integral method was used to simulate aquifer head at different distances from the stream caused by stream stage fluctuations and to estimate fluxes across the stream–aquifer boundary. Aquifer diffusivities were estimated by wiggle-matching time and amplitude of modeled response to multiple observed storm events. The peak lag time between observed stream and aquifer stage peaks ranged between 14 and 95 hour. Transient modeled diffusivity ranged from 1,000 to 7,500 m2/day and deviated from the measured and calculated single-peak stage-ratio diffusivity by 14–82 %. Stream stage fluctuation displayed more primary control over groundwater levels than recharge, especially during high-flow periods. Dam operations locally altered groundwater flow paths and velocity. The aquifer is more prone to surface-water control in the upper reaches of the pools where stream stage fluctuations are more pronounced than in the lower reaches. This method could be a useful tool for quick assessment of induced infiltration rate and bank storage related to contamination investigations or well-field management.

A time-series analysis framework for the flood-wave method to estimate groundwater model parameters

The flood-wave method is implemented within the framework of time-series analysis to estimate aquifer parameters for use in a groundwater model. The resulting extended flood-wave method is applicable to situations where groundwater fluctuations are affected significantly by time-varying precipitation and evaporation. Response functions for time-series analysis are generated with an analytic groundwater model describing stream–aquifer interaction. Analytical response functions play the same role as the well function in a pumping test, which is to translate observed head variations into groundwater model parameters by means of a parsimonious model equation. An important difference as compared to the traditional flood-wave method and pumping tests is that aquifer parameters are inferred from the combined effects of precipitation, evaporation, and stream stage fluctuations. Naturally occurring fluctuations are separated in contributions from different stresses. The proposed method is illustrated with data collected near a lowland river in the Netherlands. Special emphasis is put on the interpretation of the streambed resistance. The resistance of the streambed is the result of stream-line contraction instead of a semi-pervious streambed, which is concluded through comparison with the head loss calculated with an analytical two-dimensional cross-section model.

Residence times of stream‐groundwater exchanges due to transient stream stage fluctuations

AbstractThe biogeochemical functioning of stream ecosystems is heavily dependent on water and water‐borne nutrient fluxes between the stream itself and the streambed and banks (i.e., the hyporheic zone). The travel time of water exchanges through the hyporheic zone has been investigated previously; however, these studies have primarily modeled exchanges under steady state conditions assuming spatial pressure variations. This assumes that the hydraulic gradients that drive the exchanges are maintained the whole time the stream water remains in the bed or banks, which is unrealistic. Therefore, in this study we use a transient approach to investigate residence time distributions (RTDs) of bank inflow and bank outflow during both regular, diurnal stream stage variations and storm flow events. We demonstrate that RTDs reflect the timing and magnitude bank inflows, rather than smooth RTDs. We also show that small percentages of water from a given bank inflow event may be present in bank outflows for long periods of time, due to dispersion and diffusion within the bank, and lower rates of bank outflow, relative to bank inflow. This is apparent in the synthetic model of a single storm flow event, where 10% remained in the bank after 50 days. Additionally, residence times for a given bank inflow event are longer when repeated events occur, because the bank outflows from one event are “interrupted” by an increase in stream stage during a successive event. For example, field data capturing events of variable timing and magnitude showed that 70 days after each of three storm flow events occurred, 40, 12 and 30% of the bank inflow event remained in the banks. These cases indicate that bank exchanges are temporally dynamic and the RTDs of return flows can have significant tailing, which will dictate rates of nutrient exchange within the near‐stream environment.

Comparison of Analytical Solutions to Evaluate Aquifer Response to Arbitrary Stream Stage

Groundwater table response to arbitrarily varied stream stage is a practical engineering issue related to stream-aquifer interaction processes. A one-dimensional (1D) linear Boussinesq equation is invariably used in the interpretation. Previous studies have emphasized the employment of convolution integration and pulse or function fitting methods to solve this problem. Consequently, complicated mathematical derivations and numerical calculations are involved during an analysis. In this paper, we transformed the previously published solutions into an easily solved formation to investigate this problem. Then the solution is solved based on the trapezoidal method and applied in cases. The solution fits favorably with the previous classic solutions in the simulations of groundwater table responses to sinusoidal, linear, and unit step rise varied stream stages. This approach was also applied to interpret groundwater table fluctuations induced by typical flood waves and field measured stream stage fluctuations. The developed approach performs well compared with those solved numerically by function fitting methods and modular finite-difference flow model (MODFLOW). This analytical solution potentially provides a rapid and simple way to estimate aquifer responses to any type of stream stage variation.

Melt water driven stream and groundwater stage fluctuations on a glacier forefield (Dammagletscher, Switzerland)

In many mountain regions, large land areas with heterogeneous soils have become ice-free with the ongoing glacier retreat. On these recently formed proglacial fields, the melt of the remaining glaciers typically drives pronounced diurnal stream level fluctuations that propagate into the riparian zone. This behaviour was measured on the Damma glacier forefield in central Switzerland with stage recorders in the stream and groundwater monitoring wells along four transects. In spite of the large groundwater stage variations, radon measurements in the near-stream riparian zone indicate that there is little mixing between stream water and groundwater on daily time scales. At all four transects, including both losing and gaining reaches, the groundwater level fluctuations lagged the stream stage variations and were often damped with distance from the stream. Similar behaviours have been modelled using the diffusion equation in coastal regions influenced by tidal sea level variations. We thus tested the ability of such a model to predict groundwater level fluctuations in proglacial fields. The model reproduced several key features of the observed fluctuations at three of four locations, although discrepancies also arise due to non representative input data and model simplifications. Nevertheless, calibration of the model for the individual transects yielded realistic estimates of hydraulic diffusivities between the stream and groundwater monitoring wells. We conclude that studying diurnal groundwater fluctuations can provide important information about the subsurface hydrology of alpine watersheds dominated by glacier melt. Copyright © 2012 John Wiley & Sons, Ltd.

Riparian biogeochemical hot moments induced by stream fluctuations

Hyporheic exchanges in riparian zones induced by stream stage fluctuations, referred to as bank storage, can influence contaminant transport and transformation when mixing of groundwater and surface waters with distinct chemical signatures occur, which might lead to a high biochemical activity. The effect of bank storage on nutrient transport was analyzed here using a two‐dimensional, variably saturated and multispecies reactive transport model, which accounted for the water flow and solute transport and reactions within riparian zones. After verification with field observations, our model demonstrated that high biogeochemical activities occurred at the near‐stream riparian zone during stage fluctuation, a process referred to as bank storage hot moment (BSHM). We used Monte Carlo simulations to study the uncertainty of BSHM and related nutrient dynamics to biogeochemical and hydrological factors. The results indicated that stream fluctuations can lead to maximum bank storage volume ranging from 0 to 259 m3 m−1 of stream linear length (median = 9.7 m3 and SD = 53.2 m3). Taking denitrification as an example, BSHM can lead to considerable NO3− removal with a median removal rate of 2.1 g d−1 and SD of 17.2 g d−1 per meter of stream linear length. The NO3− uptake velocity (median = 2.7 × 10−5 and SD = 2.4 × 10−4 m min−1) was comparable to that of in‐stream transient storage from the literature. This result suggests that BSHM may be a significant process contributing to the nutrient budget at the ecosystem level. Finally, a theoretical framework representing the coupled hydrobiogeochemical controls on riparian hot spots was developed to help predicting when BSHM can become important in a particular stream.

Horizontal hydraulic conductivity of shallow streambed sediments and comparison with the grain‐size analysis results

AbstractStreambed horizontal hydraulic conductivity (Kh) has a substantial role in controlling exchanges between stream water and groundwater. We propose a new approach for determining Kh of the shallow streambed sediments. Undisturbed sediment samples were collected using tubes that were horizontally driven into streambeds. The sediment columns were analysed using a permeameter test (PT) on site. This new test approach minimizes uncertainties due to vertical flow in the vicinity of test tube and stream stage fluctuations in the computation of the Kh values. Ninety‐eight PTs using the new approach were conducted at eight sites in four tributaries of the Platte River, east‐central Nebraska, USA. The Kh values were compared with the nondirectional hydraulic conductivity values (Kg) determined from 12 empirical grain‐size analysis methods. The grain‐size analysis methods used the same sediment samples as Kh tests. Only two methods, the Terzaghi and Shepherd methods, yielded Kg values close to the Kh values. Although the Sauerbrei method produced a value relatively closer to Kh than other nine grain‐size analysis methods, the values from this method were not as reliable as the methods of Terzaghi and Shepherd due to the inconsistent fluctuation of the average estimates at each of the test sites. The Zunker, Zamarin, Hazen, Beyer, and Kozeny methods overestimated Kh, while the Slichter, US Bureau of Reclamation (USBR), Harleman, and Alyamani and Sen methods underestimated Kh. Any of these specific grain‐size methods might yield good estimates of streambed Kh at some sites, but give poor estimates at other sites, indicating that the relationship between Kg and Kh is significantly site dependent in our study. Copyright © 2011 John Wiley & Sons, Ltd.

Influence of Oscillating Flow on Hyporheic Zone Development

The hyporheic zone is an ecologically important ecotone that describes the extent to which nutrient-rich surface waters penetrate the shallow subsurface adjacent to a flowing surface water body. Although steady-state models satisfactorily explain the incursion of surface water into the subsurface as a function of head gradients developed across streambed riffles, they fail to account for the depth that surface water is observed to penetrate the subsurface or for the extent to which the hyporheic zone develops adjacent to the stream channel. To investigate these issues, transient flow modeling has been conducted at the riffle scale and supported by data for an instrumented site in northern Ontario where stream-stage fluctuations are strictly regulated. Model results show that daily stream-stage fluctuations between 0.6 and 4 m produce oscillating solute flow paths that typically reduce residence times of water and solutes in the hyporheic zone from 60 days or more under steady-state conditions to less than 1 day. Furthermore, similar stream-stage fluctuations increase the depth that solutes pervade the subsurface and banks lateral to the stream from around 1 m under steady-state conditions to as much as 2 and 10 m, respectively. The results demonstrate that the transient flow conditions triggered in the subsurface by variable stream stage can exert a strong influence on hyporheic zone development and have important implications for the hyporheos. The results are especially important for hyporheic communities that may survive gradual changes to their living conditions by migrating to more hospitable aquatic habitats, but are unable to respond to rapid changes provoked by more extreme hydrological events.

Poroelastic Loading of an Aquifer Due to Upstream Dam Releases

Short-term changes in the hydraulic head of surface water bodies are known to influence the shallow response of hydraulically connected groundwaters. Associated with these fluctuations is the physical increase in stream water creating a mechanical load on the ground surface. This load is supported by the geologic materials (sediment or rock) and the pore fluid contained within the pores. Changes in this surface load have a direct effect on the total stress of the aquifer causing either a change in effective stress or fluid pressure. This response, predicted by the framework of linear poroelasticity, is a well-understood phenomenon in geologic materials. Currently, field measurements of the hydraulic response (i.e., fluid pressure) of aquifer materials are undergoing poroelastic loading due to dam releases in the Deerfield River Watershed in Massachusetts. An increase in stream stage from upstream dam releases causes an instantaneous pore fluid pressure increase at multiple depths and locations in the aquifer. This increase lasts anywhere from 15 to 40 minutes depending on the magnitude of the rise in the stream stage. Pore-pressure changes are well correlated to stream stage fluctuations for all of the recorded events. Poroelastic models created using basin stratigraphy and hydraulic properties of the aquifer response match the field observations well. Model results suggest that the overall stratigraphy is important in controlling the magnitude and duration of the poroelastic response. An improved understanding of responses such as these can be used to constrain uncertainties in model calibration and simulations of the contaminant migration in low permeability fine-grained (compressive) materials.

Snowmelt‐induced diel fluxes through the hyporheic zone

Snowmelt processes result in diel fluctuations in streamflow and stream stage that propagate into riparian aquifers and cause a daily pumping of the hyporheic zone. This diel pumping was observed in stream stage and water table records collected in Tuolumne Meadows, Yosemite National Park, California. A model was developed using Fourier analysis to represent the stream stage fluctuations and a solution to the 1‐D, linearized Boussinesq equation for groundwater flow. The modeling demonstrates that a substantial volume of water is pumped in and out of the aquifer via this process on a daily basis. In addition, since the snowmelt‐induced groundwater fluctuations exhibit both reduced amplitudes and increased time lags at distances away from the stream, the model can be used to estimate the hydraulic parameters of the riparian aquifer. Snowmelt‐induced hyporheic pumping may have implications for biogeochemical processes in the hyporheic zone and may provide important ecosystem services related to water filtration, thermal buffering, nutrient cycling, and water quality. Consideration should be given to recognizing, quantifying, and monitoring snowmelt‐induced pumping of the hyporheic zone and the ecosystem services it provides since climate and land use changes may alter the magnitude of this process in the future.

A general framework of stream–aquifer interaction caused by variable stream stages

Stream–aquifer interface is a critical zone where surface water and groundwater exchange mass, energy, and chemicals. Previous analytical studies of stream–aquifer interaction consider stream stage fluctuations that are only functions of time. This study improves those solutions by simultaneously considering temporally and spatially variable stream stages, low-permeability streambeds, and pumping wells nearby the streams. Semi-analytical solutions of drawdown and stream–aquifer flow rate in the Laplace–Fourier domain are provided and used to obtain solutions in the real time–space domain after the inverse Laplace–Fourier transform, where the stream–aquifer flow rate refers to the rate of discharge between a stream and an adjacent aquifer. The stream–aquifer flow rate caused by the temporally variable stream stage is found to decline with time and becomes negligible when time is sufficiently long. A closed-form analytical solution for the stream–aquifer flow rate caused by a diffusive-type flood wave is obtained, and it can be used to predict the response of an aquifer upon a passing flood wave. For a diffusive-type flood wave that dies out in about 24 h, we find that the stream–aquifer flow rate drops nearly exponentially with time and dies out at about 13.4 h for a sandy aquifer and an alluvial streambed. Sensitivity analysis shows that the stream–aquifer flow rate increases with the diffusion coefficient of the flood wave ( D ) which controls the width and amplitude of the wave, and decreases with the average flood wave velocity ( v ). Low-permeability streambeds reduce stream–aquifer flow rate and also delay the response to the stream stage fluctuations. For a time-dependent cosine stream stage function with a period of 30 days, the maximal stream–aquifer flow rate with a 0.5 m thick low-permeability streambed is 24% less than that obtained without the streambed.

Groundwater head responses due to random stream stage fluctuations using basis splines

Stream‐aquifer interactions are becoming increasingly important processes in water resources and riparian management. The linearized Boussinesq equation describes the transient movement of a groundwater free surface in unconfined flow. Some standard solutions are those corresponding to an input, which is a delta function impulse, or to its integral, a unit step function in the time domain. For more complicated inputs, the response can be expressed as a convolution integral, which must be evaluated numerically. When the input is a time series of measured data, a spline function or piecewise polynomial can easily be fitted to the data. Any such spline function can be expressed in terms of a finite series of basis splines with numerical coefficients. The analytical groundwater response functions corresponding to these basis splines are presented, thus giving a direct and accurate way to calculate the groundwater response for a random time series input representing the stream stage. We use the technique to estimate responses due to a random stream stage time series and show that the predicted heads compare favorably to those obtained from numerical simulations using the Modular Three‐Dimensional Finite‐Difference Ground‐Water Flow Model (MODFLOW) simulations; we then demonstrate how to calculate residence times used for estimating riparian denitrification during bank storage.

Stream water infiltration, bank storage, and storage zone changes due to stream-stage fluctuations

During a flood period, stream-stage increases induce infiltration of stream water into an aquifer; subsequent declines in stream stage cause a reverse motion of the infiltrated water. This paper presents the results of the water exchange rate between a stream and aquifer, the storage volume of the infiltrated stream water in the surrounding aquifer (bank storage), and the storage zone. The storage zone is the part of aquifer where groundwater is replaced by stream water during the flood. MODFLOW was used to simulate stream–aquifer interactions and to quantify rates of stream infiltration and return flow. MODPATH was used to trace the pathlines of the infiltrated stream water and to determine the size of the storage zone. Simulations were focused on the analyses of the effects of the stream-stage fluctuation, aquifer properties, the hydraulic conductivity of streambed sediments, regional hydraulic gradients, and recharge and evapotranspiration (ET) rates on stream–aquifer interactions. Generally, for a given stream–aquifer system, larger flow rates result from larger stream-stage fluctuations; larger storage volumes and storage zones are produced by larger and longer-lasting fluctuations. For a given stream-stage hydrograph, a lower-permeable streambed, an aquitard, or an anisotropic aquifer of low vertical hydraulic conductivity can significantly reduce the rate of infiltration and limit the size of the storage zone. The bank storage solely caused by the stage fluctuation differs slightly between gaining and losing streams. Short-term rainfall recharge and ET loss in the shallow groundwater slightly influence on the flow rate, but their effects on bank storage in a larger area for a longer period can be considerable.

Aquifer response to stream-stage and recharge variations. II. Convolution method and applications

In this second of two papers, analytical step-response functions, developed in the companion paper for several cases of transient hydraulic interaction between a fully penetrating stream and a confined, leaky, or water-table aquifer, are used in the convolution integral to calculate aquifer heads, streambank seepage rates, and bank storage that occur in response to stream-stage fluctuations and basinwide recharge or evapotranspiration. Two computer programs developed on the basis of these step-response functions and the convolution integral are applied to the analysis of hydraulic interaction of two alluvial stream–aquifer systems in the northeastern and central United States. These applications demonstrate the utility of the analytical functions and computer programs for estimating aquifer and streambank hydraulic properties, recharge rates, streambank seepage rates, and bank storage. Analysis of the water-table aquifer adjacent to the Blackstone River in Massachusetts suggests that the very shallow depth of water table and associated thin unsaturated zone at the site cause the aquifer to behave like a confined aquifer (negligible specific yield). This finding is consistent with previous studies that have shown that the effective specific yield of an unconfined aquifer approaches zero when the capillary fringe, where sediment pores are saturated by tension, extends to land surface. Under this condition, the aquifer's response is determined by elastic storage only. Estimates of horizontal and vertical hydraulic conductivity, specific yield, specific storage, and recharge for a water-table aquifer adjacent to the Cedar River in eastern Iowa, determined by the use of analytical methods, are in close agreement with those estimated by use of a more complex, multilayer numerical model of the aquifer. Streambank leakance of the semipervious streambank materials also was estimated for the site. The streambank-leakance parameter may be considered to be a general (or lumped) parameter that accounts not only for the resistance of flow at the river–aquifer boundary, but also for the effects of partial penetration of the river and other near-stream flow phenomena not included in the theoretical development of the step-response functions.

Effect of Shallow Penetration and Streambed Sediments on Aquifer Response to Stream Stage Fluctuations (Analytical Model)

AbstractAn analytical model of stream‐aquifer interaction is proposed that considers the effects from a small degree of aquifer penetration and low‐permeability sediments on the head response to an arbitrary stream‐stage hydrograph. Aquifer sections under the stream and beyond are considered in a single model. The model of ground water flow in the aquifer is based on the Dupuit assumptions corrected for leakage from the stream. The model can use stream‐stage hydrographs in both analytical and tabular forms. The nondimensional linear boundary value problem is solved for hydraulic head in the aquifer using numerical Laplace transforms and a convolution algorithm. The proposed solution is used to assess the impact of shallow penetration and low‐permeability streambed sediments on head responses by comparison with available solutions which neglect these factors.

Spectral and bispectral analysis for single‐ and multiple‐input nonlinear phreatic aquifer systems

In general, stochastic partial differential equations and/or boundary conditions describing flow in phreatic aquifers are nonlinear. This paper uses second‐order perturbation to approximate the response of a phreatic aquifer system subject to multiple random inputs. The approach is equivalent to assuming quadratic nonlinearities in the original nonlinear phreatic aquifer system. Using frequency domain representations, the resulting model is decomposed into linear and nonlinear (quadratic) frequency response functions (FRF). For Gaussian input, the response of a nonlinear phreatic aquifer system is non‐Gaussian and is typically skewed. Thus the variance spectrum is insufficient to describe the response process. The bispectrum, defined as the Fourier transform of the third‐order cumulant sequence, represents the distribution of skewness with frequency and further serves as a measure of the nonlinearity of the system. Given input processes of aquifer recharge and stream stage fluctuations, the linear and quadratic FRF are used to construct the spectrum and bispectrum of the response process. The role of nonlinearity in a stream‐aquifer system is examined.